2025/09/23 by Sourav Chatterjee, Chatterjee, Sourav, Oren Yakir +1 · 1 citation
Physics and Astronomy · Mathematics · #Quantum Chromodynamics and Particle Interactions #High-Energy Particle Collisions Research #Random Matrices and Applications
paper · pdf · doi:10.48550/arxiv.2509.19176
We study the lattice Yang-Mills-Higgs model with inverse gauge coupling β>0 and Higgs length α>0, in the ``complete breakdown of symmetry" regime. For lattice dimension d≥ 2 and (abelian) gauge group U(1), we prove that for any m>0, if α= mβ and β is large enough, the model exhibits exponential decay of correlations. This extends the classical result of Osterwalder and Seiler (1978), who required in addition that m be sufficiently large. Our result also verifies a phase diagram from the physics literature, predicted by Fradkin and Shenker (1979). The proof is based on the Glimm-Jaffe-Spencer cluster expansion around a massive Gaussian field, following the approach of Balaban et al. (1984).